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 Feb 23 accepted Eliminating an inner sum for a double sum Feb 23 comment Eliminating an inner sum for a double sum @AndréNicolas L = floor(N/k) if that matters Feb 23 asked Eliminating an inner sum for a double sum Feb 23 accepted A way to simplify $\gcd(a,b)$ condition in a double sum? Feb 22 accepted Reducing this sum to closed form Feb 22 awarded Commentator Feb 22 comment Reducing this sum to closed form Feb 22 comment Reducing this sum to closed form Do I absolutely have to multiply everything out? I had done so on Wolfram and it looked quite long and unreadable. You are saying I have to multiply it all out and then sum each piece separately? Feb 22 revised Reducing this sum to closed form edited tags Feb 22 asked Reducing this sum to closed form Feb 22 comment A way to simplify $\gcd(a,b)$ condition in a double sum? @IvanLoh And how do you transform the (L+1-b) to that phi(n) expression in the third step? Where did b go? Feb 22 comment A way to simplify $\gcd(a,b)$ condition in a double sum? @IvanLoh Where does L^2+2 come from Feb 22 awarded Scholar Feb 22 awarded Editor Feb 22 revised A way to simplify $\gcd(a,b)$ condition in a double sum? added 151 characters in body Feb 22 asked A way to simplify $\gcd(a,b)$ condition in a double sum? Jul 2 comment Trying to find the name of this Nim variant @StevenStadnicki My $S$ would be dynamic then, since there would be times when taking $x$ stones from the pile is OK in one instance but not in another, since the end result must be a part of $V$. Jul 2 comment Trying to find the name of this Nim variant @StevenStadnicki I vaguely understand it as the distance from winning position (a grundy number of 1 meaning you're one step away from a winning position or something to this effect). I am also not sure about periods, since my set $V$ has an exponential recurrence Jul 2 comment Trying to find the name of this Nim variant In my case, $V$ follows a recurrence. My issue is that I don't even know where to begin analyzing in order to develop a strategy that doesn't rely on brute scanning/trial and error/etc. Jul 2 comment Trying to find the name of this Nim variant However it is not a standard subtraction game, which is what my question is about. In my particular case, not all states of the pile are valid.